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Geometric multiaxial representation of N-qubit mixed symmetric separable states

Suma, S.P.; Sirsi, Swarnamala; Hegde, Subramanya; Bharath, Karthik

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Authors

S.P. Suma

Swarnamala Sirsi

Subramanya Hegde



Abstract

Study of an N qubit mixed symmetric separable states is a long standing challenging problem as there exist no unique separability criterion. In this regard, we take up the N-qubit mixed symmetric separable states for a detailed study as these states are of experimental importance and offer elegant mathematical analysis since the dimension of the Hilbert space reduces from 2N to N + 1. Since there exists a one to one correspondence between spin-j system and an N-qubit symmetric state, we employ Fano statistical tensor parameters for the parametrization of spin density matrix. Further, we use geometric multiaxial representation (MAR) of density matrix to characterize the mixed symmetric separable states. Since separability problem is NP hard, we choose to study it in the continuum limit where mixed symmetric separable states are characterized by the P-distribution function λ (ᶿ, Φ) We show that the N-qubit mixed symmetric separable state can be visualized as a uniaxial system if the distribution function is independent of ᶿ, and Φ. We further choose distribution function to be the most general positive function on a sphere and observe that the statistical tensor parameters characterizing the N-qubit symmetric system are the expansion coefficients of the distribution function. As an example for the discrete case, we investigate the MAR of a uniformly weighted two qubit mixed symmetric separable state. We also observe that there exists a correspondence between separability and classicality of states.

Journal Article Type Article
Acceptance Date Aug 19, 2017
Publication Date Aug 30, 2017
Deposit Date Aug 23, 2017
Publicly Available Date Aug 30, 2017
Journal Physical Review A
Print ISSN 2469-9926
Electronic ISSN 2469-9934
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 96
Issue 2
Article Number 022328
DOI https://doi.org/10.1103/PhysRevA.96.022328
Public URL https://nottingham-repository.worktribe.com/output/879566
Publisher URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.022328
Additional Information ©2017 American Physical Society

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